Structured pathway across the transition state for peptide folding revealed by molecular dynamics simulations.

Interdisciplinary Center for Scientific Computing, University of Heidelberg, Heidelberg, Germany.

Abstract

Small globular proteins and peptides commonly exhibit two-state folding kinetics in which the rate limiting step of folding is the surmounting of a single free energy barrier at the transition state (TS) separating the folded and the unfolded states. An intriguing question is whether the polypeptide chain reaches, and leaves, the TS by completely random fluctuations, or whether there is a directed, stepwise process. Here, the folding TS of a 15-residue β-hairpin peptide, Peptide 1, is characterized using independent 2.5 μs-long unbiased atomistic molecular dynamics (MD) simulations (a total of 15 μs). The trajectories were started from fully unfolded structures. Multiple (spontaneous) folding events to the NMR-derived conformation are observed, allowing both structural and dynamical characterization of the folding TS. A common loop-like topology is observed in all the TS structures with native end-to-end and turn contacts, while the central segments of the strands are not in contact. Non-native sidechain contacts are present in the TS between the only tryptophan (W11) and the turn region (P7-G9). Prior to the TS the turn is found to be already locked by the W11 sidechain, while the ends are apart. Once the ends have also come into contact, the TS is reached. Finally, along the reactive folding paths the cooperative loss of the W11 non-native contacts and the formation of the central inter-strand native contacts lead to the peptide rapidly proceeding from the TS to the native state. The present results indicate a directed stepwise process to folding the peptide.

a) Backbone snapshot of Peptide 1 extracted at the end of the simulation started from the NMR structure. For clarity only the C atoms are shown. b) Contour map of the free energy change, A, as a function of the position in the -R plane (fraction of native contacts, , within the peptide - R parameter). is calculated with respect to the state with the highest probability, i.e., the -hairpin state. Three distinct states can be identified. The states with the two deep minima are the unfolded (U) and folded (F) states and the saddle point corresponds to the single transition state (TS), i.e., the barrier that all molecules must cross if they are to fold to the native state. The F, U and TS states were defined as follows: F comprises all structures populating the basin around the global minimum at = 0.85 and R = 4.95, and with free energy values within 12 kJ/mol from the global minimum; U comprises all structures populating the basin around the local minimum at = 0.10 and R = 2.10, and also with free energy values up to 12 kJ/mol; the structures at the top of the barrier, i.e., not belonging to F or U, were assigned to the TS.

a) Time convergence of the A for two typical grid cells in the -R free energy landscape: One cell in the U state around the local minimum with A 2 kJ/mol (solid line), and the other cell in the TS region with A 14 kJ/mol (dashed line). b) Probability distribution of the free energy standard deviations, , for all the grid cells of the free energy landscape.

a) Schematic diagram showing the possible scenarios for the paths reaching the TS, namely: reactive and non-reactive paths; in the reactive paths, the crossing of the TS can occur either from U to F (forward reactive path) or from F to U (backward reactive path); in non-reactive paths, the peptide falls back into the state of origin (either UTSU or FTSF paths). b) Time evolution of the peptide through the U, TS and F states for six representative paths along the simulations. The three rows in each panel represent the existence of the U (unfolded), T (transition) and F (folded) states. All the four scenarios described in panel a can be observed. The top and middle panels show the forward and backward reactive paths, respectively. The bottom panels show the non-reactive paths, either UTSU or FTSF paths.

Distribution of TS lifetimes, defined as the mean residence time in TS, for Peptide 1 (solid line). The dashed line shows a mono-exponential fit to the data. The error bars represent one standard deviation. The time constant of the exponential fit is taken as the average lifetime of the TS.

a) Distributions of the distances between the C atoms of residues N6-G9 (top), I4-T12 (middle) and S1-E15(bottom) in the TSE. The corresponding distributions in the F state are shown as green filled bars. b) Distributions of the minimum distances between the atoms of the W11 sidechain and the atoms of the sidechain of two turn residues, namely P7 (top) and G9 (bottom) in the TSE. The corresponding distributions in the F state are shown as green filled bars. Snapshot of TS structure at left shows the key-lock configuration of W11 with P7 and G9 residues, while folded structure at the right has W11 in native configuration.

Distribution of various topological features in U-TS-F, F-TS-U, U-TS-U and F-TS-F subpopulations of the TSE of Peptide 1.

Distributions of the distance between the C- atoms of the residues N6-G9 (first row), Y4-Y12 (second row), S1-E15 (third row). Distributions of the minimum distances between the atoms of the W11 sidechain and the atoms of the sidechain of two turn residues, namely P7 (fourth row) and G9 (fifth row). The F-TS-F subpopulation shown in brown color corresponds to the structures with middle backbone contacts formed.

Time evolution of the minimum distance between all the atoms of the W11 sidechain and all the atoms of the P7 sidechain (maroon) for a representative reactive path.

In addition, the distances between the C atoms of the turn (N6-G9) and central (I4-T12) residues are shown in black and blue, respectively. The shaded region represents the TS. The three histograms at the bottom show the distributions of the minimum distances between the W11 and P7 sidechains for the structures sampled before the TS (prior-to-TS), in the TS (TS) and in the native (F) state evaluated over all forward reactive paths. For the prior-to-TS ensemble the structures occurring within 1 ns prior to the TS along all forward reactive paths are taken.

The mechanism by which the peptide crosses TS is shown. The TS is reached with the formation of native end-to-end (red) and turn (green) contacts, with the end-to-end formation appearing at the TS, making it the unique feature of the TS of Peptide 1. However, reaching the folded state from the TS involves W11 sidechain (purple) repositioning and concomitant native arrangement of the central segment (orange) of -hairpin. In “Prior-to-TS” and TS, W11 is in a ‘key-lock’ configuration with turn residues, thus from a dynamic point of view it acts as a chaperone to reach the TS, while the last stage to reach the native state involves ‘correct’ native arrangement of W11 with the central segment of -hairpin (See representative structures).